To install Snow Leopard you want to make sure you meet the system requirements: http://support.apple.com/kb/SP575
Going to Apple > About this mac will tell you if you have the required Intel Processor and the 1 GB RAM.
Also check to make sure you have the require 5 GB minimum of free space on your computer.
Before installing a new operating system, make sure you have a backup of your data: http://support.apple.com/kb/ht1427.
Yes, and 10.6.8 should be as far as you go.
You can do 10.7, but I advise against it for 10.5 era machines as it slows them down and breaks a good portion of users software and third party hardware drivers, the PPC based stuff that floated around a lot for 10.5 and 10.6.
10.6 will run your PPC based code using Rosetta, in 10.7 there is no Rosetta, so you'll have a slow machine and have to buy new software and even new hardware like printers etc.
10.8 is coming out this summer, your 10.5 machine is likely at it's end of life stage, so milk 10.6.8 for as long as you can then buy a new box and new software, IMO. Skip the sick kitty that's Lion.
I am currently undergoing the same process.
It's a royal pain that you cannot order the upgrade direct from Apple online as you can with Mountain Lion.
Is the only real way to call them up for the order?
I am also currently extracting the installESD.dmg from a Mountain Lion I have purchased for my other mac and mounting it as a back up USB. I have been informed that I can update from my 10.5.8 to the Snow Leopard 10.6 - does this make sense??
You can upgrade fro 10.5 to 10.6 no problem, but the only source of the DVD is by phone.
In the US, call 1-800-MY-APPLE and ask for a sales assistant. Last quoted price was $19.99 for the single-user and $29.99 for the family licence.
For other countries, check here; http://support.apple.com/kb/HE57
Don't forget to ask for Sales; the tech support guys can't help.
Once installed you can go to 10.6.8 with the combo installer; http://support.apple.com/kb/DL1399
Which gets you the App Store.
I can't help as far as the ML idea is concerned, but maybe someone else can.
Well, I too own a version 7.1 iMac from late 2007, and I am currently running Mountain Lion with rather good system speed. I mainly chaulk the reasonable speed of my system with Mountain Lion up to the fact that after installing Mountain Lion, from Lion which also ran fine, I entered the Mountain Lion Recovery Partition and its "Disk Utility", where I ran "Repair Disk" and then I ran "Repair Permissions" twice. This was intended to stabilize the system's OS fully. This combined with running the full 6 GB of RAM that this model of iMac can use up to has resulted in a very satisfying User experience with ML 10.8.2. (OWC, a popular vendor online, has rigorously tested this model, version 7.1, with 6 GB of RAM and its runs fully stably, even though Apple only rates it up to 4 GB of RAM.)
Hope this helps